Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/00207721.2021.2023689 http://hdl.handle.net/11449/233996 |
Resumo: | This note is concerned with conditions on a set of non-singular matrices (Formula presented.), (Formula presented.), so that any convex combination of these matrices is also non-singular. The first part of the note points out that Theorem 2.3 in a previous paper [Beteto et al. (2021). Less conservative conditions for robust LQR-state derivative controller design: An LMI approach. International Journal of Systems Science] provides only necessary conditions, which are not sufficient in the general case. In the second part, some stability results based on Linear Matrix Inequalities (LMIs) for a class of fractional order systems are used to establish new sufficient conditions. Numerical examples are presented for illustration. The results suggest that the new LMI conditions may be less conservative compared to a test proposed in the literature on P-matrices, and also to a positive-definiteness test based on matrix cross-products. |
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Repositório Institucional da UNESP |
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Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matricesfull rank conditions of convex combinations of matriceslinear matrix inequalities (LMIs)Linear quadratic regulator (LQR)robust controlstate derivative feedback (SDF)This note is concerned with conditions on a set of non-singular matrices (Formula presented.), (Formula presented.), so that any convex combination of these matrices is also non-singular. The first part of the note points out that Theorem 2.3 in a previous paper [Beteto et al. (2021). Less conservative conditions for robust LQR-state derivative controller design: An LMI approach. International Journal of Systems Science] provides only necessary conditions, which are not sufficient in the general case. In the second part, some stability results based on Linear Matrix Inequalities (LMIs) for a class of fractional order systems are used to establish new sufficient conditions. Numerical examples are presented for illustration. The results suggest that the new LMI conditions may be less conservative compared to a test proposed in the literature on P-matrices, and also to a positive-definiteness test based on matrix cross-products.Electronic Engineering Division Instituto Tecnológico de Aeronáutica (ITA), SPDepartment of Electrical Engineering São Paulo State University (UNESP) School of Engineering, SPFaculty of Mathematics and Computer Science Adam Mickiewicz UniversityDepartment of Electrical Engineering São Paulo State University (UNESP) School of Engineering, SPInstituto Tecnológico de Aeronáutica (ITA)Universidade Estadual Paulista (UNESP)Adam Mickiewicz UniversityGalvão, Roberto Kawakami HarropTeixeira, Marcelo Carvalho Minhoto [UNESP]Szulc, TomaszAssunção, Edvaldo [UNESP]Beteto, Marco Antonio Leite [UNESP]2022-05-01T12:09:42Z2022-05-01T12:09:42Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/00207721.2021.2023689International Journal of Systems Science.1464-53190020-7721http://hdl.handle.net/11449/23399610.1080/00207721.2021.20236892-s2.0-85122689884Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Systems Scienceinfo:eu-repo/semantics/openAccess2022-05-01T12:09:42Zoai:repositorio.unesp.br:11449/233996Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-05-01T12:09:42Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
title |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
spellingShingle |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices Galvão, Roberto Kawakami Harrop full rank conditions of convex combinations of matrices linear matrix inequalities (LMIs) Linear quadratic regulator (LQR) robust control state derivative feedback (SDF) |
title_short |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
title_full |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
title_fullStr |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
title_full_unstemmed |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
title_sort |
Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices |
author |
Galvão, Roberto Kawakami Harrop |
author_facet |
Galvão, Roberto Kawakami Harrop Teixeira, Marcelo Carvalho Minhoto [UNESP] Szulc, Tomasz Assunção, Edvaldo [UNESP] Beteto, Marco Antonio Leite [UNESP] |
author_role |
author |
author2 |
Teixeira, Marcelo Carvalho Minhoto [UNESP] Szulc, Tomasz Assunção, Edvaldo [UNESP] Beteto, Marco Antonio Leite [UNESP] |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Instituto Tecnológico de Aeronáutica (ITA) Universidade Estadual Paulista (UNESP) Adam Mickiewicz University |
dc.contributor.author.fl_str_mv |
Galvão, Roberto Kawakami Harrop Teixeira, Marcelo Carvalho Minhoto [UNESP] Szulc, Tomasz Assunção, Edvaldo [UNESP] Beteto, Marco Antonio Leite [UNESP] |
dc.subject.por.fl_str_mv |
full rank conditions of convex combinations of matrices linear matrix inequalities (LMIs) Linear quadratic regulator (LQR) robust control state derivative feedback (SDF) |
topic |
full rank conditions of convex combinations of matrices linear matrix inequalities (LMIs) Linear quadratic regulator (LQR) robust control state derivative feedback (SDF) |
description |
This note is concerned with conditions on a set of non-singular matrices (Formula presented.), (Formula presented.), so that any convex combination of these matrices is also non-singular. The first part of the note points out that Theorem 2.3 in a previous paper [Beteto et al. (2021). Less conservative conditions for robust LQR-state derivative controller design: An LMI approach. International Journal of Systems Science] provides only necessary conditions, which are not sufficient in the general case. In the second part, some stability results based on Linear Matrix Inequalities (LMIs) for a class of fractional order systems are used to establish new sufficient conditions. Numerical examples are presented for illustration. The results suggest that the new LMI conditions may be less conservative compared to a test proposed in the literature on P-matrices, and also to a positive-definiteness test based on matrix cross-products. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-05-01T12:09:42Z 2022-05-01T12:09:42Z 2022-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1080/00207721.2021.2023689 International Journal of Systems Science. 1464-5319 0020-7721 http://hdl.handle.net/11449/233996 10.1080/00207721.2021.2023689 2-s2.0-85122689884 |
url |
http://dx.doi.org/10.1080/00207721.2021.2023689 http://hdl.handle.net/11449/233996 |
identifier_str_mv |
International Journal of Systems Science. 1464-5319 0020-7721 10.1080/00207721.2021.2023689 2-s2.0-85122689884 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Systems Science |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799965178581745664 |